EduSahara™ Worksheet

Question 1

1.

A chord that passes through the centre of the circle is called

(i)

diameter
(ii)

segment
(iii)

radius
(iv)

chord
(v)

semi-circle

Question 2

2.

A chord of a circle divides the whole circular region into two parts, each called a

(i)

radius
(ii)

circumference
(iii)

chord
(iv)

segment
(v)

diameter

Question 3

3.

The segment of the circle containing the centre of the circle is called

(i)

radius
(ii)

chord
(iii)

major segment
(iv)

centre
(v)

segment

Question 4

4.

Which of the following statements are true?

a)	A line can meet a circle atmost at two points.
b)	Every circle has a unique centre.
c)	Every circle has a unique diameter.
d)	Each radius of a circle is also a chord of the circle.
e)	A circle consists of an infinite number of points.

(i)

{c,a}
(ii)

{d,b}
(iii)

{a,b,e}
(iv)

{c,a,b}
(v)

{c,d,e}

Question 5

5.

Which of the following statements are true?

a)	An infinite number of chords may be drawn for a circle.
b)	One and only one tangent can be drawn to a circle from a point outside it.
c)	Every circle has a unique diameter.
d)	Two semi-circles of a circle together make the whole circle.
e)	An infinite number of diameters may be drawn for a circle.

(i)

{c,d}
(ii)

{a,d,e}
(iii)

{b,a}
(iv)

{b,c,e}
(v)

{b,a,d}

Question 6

6.

In the given triangle S is the circumcentre. If SG = 13.80 cm, find the circumference of the circumcircle

(i)

84.7 cm
(ii)

86.7 cm
(iii)

87.7 cm
(iv)

88.7 cm
(v)

85.7 cm

Question 7

7.

Find the side of the square in the following figure if the radius of the circle is 11.00 cm.

(i)

15.55 cm
(ii)

16.55 cm
(iii)

17.55 cm
(iv)

14.55 cm
(v)

13.55 cm

Question 8

8.

If a chord CD = 15 cm is drawn in a circle with radius OC = 11 cm, find its distance from the centre of the circle

(i)

9.05 cm
(ii)

10.05 cm
(iii)

7.05 cm
(iv)

8.05 cm
(v)

6.05 cm

Question 9

9.

The diameter JK of a circle with centre 'O' is perpendicular to the chord HI. If HI = 18.00 cm and JL = 2.81 cm, find the radius of the circle.

(i)

16.81 cm
(ii)

14.81 cm
(iii)

15.81 cm
(iv)

17.81 cm
(v)

13.81 cm

Question 10

10.

'E' and 'F' are centres of circles of radii 2 cm and 9 cm such that EF = 17 cm and 'G' is the centre of the circle of radius 'r' cm which touches the above circles externally. If ∠EGF = 90°, find 'r'

(i)

5 cm
(ii)

6 cm
(iii)

4 cm
(iv)

7 cm
(v)

8 cm

Question 11

11.

Which of the following statements are true?

a)	A chord divides a circle into two segments.
b)	The radius is the shortest chord.
c)	A chord divides a circle into two sectors.
d)	Atmost one chord can be drawn on a circle with a certain length.
e)	The diameter is the longest chord.

(i)

{b,a}
(ii)

{d,b,a}
(iii)

{c,e,a}
(iv)

{c,e}
(v)

{a,e}

Question 12

12.

Which of the following statements are true?

a)	No two chords bisects each other.
b)	Equal length chords subtend equal angles at the centre of the circle.
c)	Equal length chords are equidistant from the centre of the circle.
d)	The longest chord of the circle passes through the centre of the circle.
e)	The farther the chord is from the centre, the larger the angle it subtends at the centre.

(i)

{a,b}
(ii)

{b,c,d}
(iii)

{a,b,c}
(iv)

{a,e,d}
(v)

{e,c}

Question 13

13.

Which of the following statements are true?

a)	A sector is the area enclosed by two radii and a chord.
b)	A circle divides the plane on which it lies into three parts.
c)	The area enclosed by a chord and its major arc is called major segment.
d)	The diameter divides the circle into two unequal parts.
e)	The area enclosed by a chord and its minor arc is called minor segment.

(i)

{a,b}
(ii)

{a,d,e}
(iii)

{b,c,e}
(iv)

{a,b,c}
(v)

{d,c}

Question 14

14.

Which of the following statements are true?

a)	The midpoint of any diameter of a circle is its centre.
b)	Two chords bisect each other.
c)	The longest of all chords of a circle is called diameter.
d)	The diameter divides the circle into two unequal parts.
e)	A sector is the area enclosed by two radii and a chord.

(i)

{a,c}
(ii)

{e,b,a}
(iii)

{d,c}
(iv)

{b,a}
(v)

{d,c,a}

Question 15

15.

Which of the following statements are true?

a)	A radius is a limiting case of a diameter.
b)	A secant and a chord are same.
c)	A secant has two end points.
d)	A tangent is the limiting case of a secant.
e)	A diameter is a limiting case of a chord.

(i)

{b,e}
(ii)

{a,d}
(iii)

{b,e,d}
(iv)

{c,a,d}
(v)

{d,e}

Question 16

16.

JK , LM , NO , PQ are chords of a circle with JK = 5 cm , LM = 2 cm , NO = 5.6 cm and PQ = 7.06 cm. The chord farthest from the centre of the circle is

(i)

JK = 5 cm
(ii)

PQ = 7.06 cm
(iii)

LM = 2 cm
(iv)

NO = 5.6 cm

Question 17

17.

In the given figure, F and G are centres of two circles with equal radii intersecting at H and I. If FG = 20 cm and HI = 10.2 cm, find the radii of the circles

(i)

10.23 cm
(ii)

11.23 cm
(iii)

12.23 cm
(iv)

13.23 cm
(v)

9.23 cm

Question 18

18.

In the given figure, two circles of radii JL = 12.4 cm & KL = 12.4 cm intersect at L & M. The distance between the centres JK = 20 cm, find the length of LM

(i)

16.66 cm
(ii)

13.66 cm
(iii)

15.66 cm
(iv)

12.66 cm
(v)

14.66 cm

Question 19

19.

In the given figure, O is the centre of the circle. L is a point on chord JK such that JL = LK. Find ∠OLJ

(i)

100°
(ii)

120°
(iii)

95°
(iv)

90°
(v)

105°

Question 20

20.

JK is a line segment and M is its mid-point. Three semi-circles are drawn with JM , MK and JK as diameters. L , N and M respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given JL = 7 cm